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Motivated by the large branching fractions of $J/\psi \to f_0 (1710)\omega/f_0(1710) \phi$ and the light exotic candidates, we find that there mayexist molecular states composed of $f_0(1710) \omega$ and $f_0 (1710) \phi$,which correspond to $X(2440)$ and $X(2680)$ observed in a few decades before.The branching fraction of $X(2440)$ and $X(2680)$ to various $PV$ channels and$KK\omega(\phi)$ channels are estimated in the molecular scenario. In addition,the large branching fractions of $J/\psi \to f_0 (1710) \omega/f_0(1710) \phi$indicate the sizable molecular components in the $J/\psi$ state. Thus, weconsider the $J/\psi$ as the supperposition of $c\bar{c}(1S)$, $f_0(1710)\omega$ and $f_0 (1710) \phi$ molecular states, and these molecular componentshave significant impact on the light hadron decays of $J/\psi$, which mayshield light on the long standing $\rho-\pi$ puzzle.

Molecular components in the $J/\psi$ and the $\rho$-$\pi$ puzzle